60edo
IMPORTED REVISION FROM WIKISPACES
This is an imported revision from Wikispaces. The revision metadata is included below for reference:
- This revision was by author genewardsmith and made on 2014-07-21 12:16:12 UTC.
- The original revision id was 516709504.
- The revision comment was:
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.
Original Wikitext content:
The 60 equal division divides the octave into 60 parts of exactly 20 cents each. Since 60 = 5 * 12, it belongs to the family of edos which contain 12edo, and like the other small edos of this kind, it tempers out the [[Pythagorean comma]], 531441/524288 = |-19 12>. In the 5-limit, it tempers out both the magic comma, 3125/3072, and the amity comma, 1600000/1594323, and supplies the optimal patent val for 5-limit magic, tempering out 3125/3072. In the 7-limit it tempers out 875/864, 245/243, 225/224 and 10976/10935, and supports magic, compton and tritonic temperaments. In the 11-limit, the 60e val scores lower in badness than the patent val, and makes for an excellent tritonic tuning. It tempers out 121/120 and 441/440, whereas the patent val tempers out 100/99, 385/384 and 540/539. The tuning of 13 is superb at half a cent flat, and the 60e val also works excellently for 13-limit tritonic. As a no-fives val, it is also excellent for the 2.3.7.11.13 [[Chromatic pairs#Bleu|bleu temperament]]. =Intervals= || degrees of 60edo || cents value || approximate ratios in the 2.3.5.13 subgroup || additional ratios of 7 and 11 (assuming flat values for primes) || || 0 || 0 || || || || 1 || 20 || || || || 2 || 40 || || || || 3 || 60 || || || || 4 || 80 || || || || 5 || 100 || || || || 6 || 120 || 16/15 || || || 7 || 140 || || || || 8 || 160 || || 12/11, 11/10 || || 9 || 180 || 10/9 || || || 10 || 200 || 9/8 || || || 11 || 220 || || || || 12 || 240 || 15/13 || 8/7 || || 13 || 260 || || 7/6 || || 14 || 280 || || || || 15 || 300 || || || || 16 || 320 || || || || 17 || 340 || || 11/9 || || 18 || 360 || 16/13 || || || 19 || 380 || || || || 20 || 400 || || || || 21 || 420 || || 14/11 || || 22 || 440 || || 9/7 || || 23 || 460 || 13/10 || || || 24 || 480 || || || || 25 || 500 || 4/3 || || || 26 || 520 || || || || 27 || 540 || || 11/8, 15/11 || || 28 || 560 || 18/13 || || || 29 || 580 || || 7/5 || || 30 || 600 || || || || 31 || 620 || || 10/7 || || 32 || 640 || 13/8 || || || 33 || 660 || || 16/11, 22/15 || || 34 || 680 || || || || 35 || 700 || 3/2 || || || 36 || 720 || || || || 37 || 740 || 20/13 || || || 38 || 760 || || 14/9 || || 39 || 780 || || 11/7 || || 40 || 800 || || || || 41 || 820 || || || || 42 || 840 || 13/8 || || || 43 || 860 || || 18/11 || || 44 || 880 || || || || 45 || 900 || || || || 46 || 920 || || || || 47 || 940 || || 12/7 || || 48 || 960 || 26/15 || 7/4 || || 49 || 980 || || || || 50 || 1000 || 16/9 || || || 51 || 1020 || 9/5 || || || 52 || 1040 || || 11/6, 20/11 || || 53 || 1060 || || || || 54 || 1080 || 15/8 || || || 55 || 1100 || || || || 56 || 1120 || || || || 57 || 1140 || || || || 58 || 1160 || || || || 59 || 1180 || || || || 60 || 1200 || || || =Compositions= [[http://eceserv0.ece.wisc.edu/%7Esethares/mp3s/rojqoq.html|Rojqoq (So-Called Peace)]] [[http://micro.soonlabel.com/gene_ward_smith/Others/Sethares/Rojqoq.mp3|play]] by William Sethares [[http://youtu.be/1rrgmP9VYQU|Skating On Thin Ice]] [[http://micro.soonlabel.com/gene_ward_smith/Others/Perry/Skating%20On%20Thin%20Ice.mp3|play]] [[http://youtu.be/5GIZOYMkkJ0|My Mother Said So]] [[http://micro.soonlabel.com/gene_ward_smith/Others/Perry/My%20Mother%20Said%20So.mp3|play]] [[http://www.macjams.com/song/62273|Black Salt - White Pepper]] [[http://micro.soonlabel.com/gene_ward_smith/Others/Perry/Black%20Salt%20-%20White%20Pepper.mp3|play]] [[http://www.macjams.com/song/64413|NGC 300]][[http://micro.soonlabel.com/gene_ward_smith/Others/Perry/NGC%20300.mp3|play]] all by Robin Perry [[http://x31eq.com/music/dingshi.mp3|Dingshi]] and [[http://x31eq.com/music/jitter.ogg|Gene's Jitterbug (ogg)]] [[http://micro.soonlabel.com/gene_ward_smith/Others/Breed/jitter.mp3|Gene's Jitterbug (mp3)]] [[http://x31eq.com/music/jitter60.pdf|Score]] by Graham Breed =Images= [[image:60edo wheel with cents values.png width="560" height="560"]] [[image:blue_60edo.png]] [[image:60edoguitar.jpg]] Robin Perry guitar
Original HTML content:
<html><head><title>60edo</title></head><body><br />
The 60 equal division divides the octave into 60 parts of exactly 20 cents each. Since 60 = 5 * 12, it belongs to the family of edos which contain 12edo, and like the other small edos of this kind, it tempers out the <a class="wiki_link" href="/Pythagorean%20comma">Pythagorean comma</a>, 531441/524288 = |-19 12>. In the 5-limit, it tempers out both the magic comma, 3125/3072, and the amity comma, 1600000/1594323, and supplies the optimal patent val for 5-limit magic, tempering out 3125/3072. In the 7-limit it tempers out 875/864, 245/243, 225/224 and 10976/10935, and supports magic, compton and tritonic temperaments. In the 11-limit, the 60e val scores lower in badness than the patent val, and makes for an excellent tritonic tuning. It tempers out 121/120 and 441/440, whereas the patent val tempers out 100/99, 385/384 and 540/539. The tuning of 13 is superb at half a cent flat, and the 60e val also works excellently for 13-limit tritonic. As a no-fives val, it is also excellent for the 2.3.7.11.13 <a class="wiki_link" href="/Chromatic%20pairs#Bleu">bleu temperament</a>.<br />
<br />
<!-- ws:start:WikiTextHeadingRule:0:<h1> --><h1 id="toc0"><a name="Intervals"></a><!-- ws:end:WikiTextHeadingRule:0 -->Intervals</h1>
<table class="wiki_table">
<tr>
<td>degrees of 60edo<br />
</td>
<td>cents value<br />
</td>
<td>approximate ratios in the 2.3.5.13 subgroup<br />
</td>
<td>additional ratios of 7 and 11 (assuming flat values for primes)<br />
</td>
</tr>
<tr>
<td>0<br />
</td>
<td>0<br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>1<br />
</td>
<td>20<br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>2<br />
</td>
<td>40<br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>3<br />
</td>
<td>60<br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>4<br />
</td>
<td>80<br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>5<br />
</td>
<td>100<br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>6<br />
</td>
<td>120<br />
</td>
<td>16/15<br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>7<br />
</td>
<td>140<br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>8<br />
</td>
<td>160<br />
</td>
<td><br />
</td>
<td>12/11, 11/10<br />
</td>
</tr>
<tr>
<td>9<br />
</td>
<td>180<br />
</td>
<td>10/9<br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>10<br />
</td>
<td>200<br />
</td>
<td>9/8<br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>11<br />
</td>
<td>220<br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>12<br />
</td>
<td>240<br />
</td>
<td>15/13<br />
</td>
<td>8/7<br />
</td>
</tr>
<tr>
<td>13<br />
</td>
<td>260<br />
</td>
<td><br />
</td>
<td>7/6<br />
</td>
</tr>
<tr>
<td>14<br />
</td>
<td>280<br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>15<br />
</td>
<td>300<br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>16<br />
</td>
<td>320<br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>17<br />
</td>
<td>340<br />
</td>
<td><br />
</td>
<td>11/9<br />
</td>
</tr>
<tr>
<td>18<br />
</td>
<td>360<br />
</td>
<td>16/13<br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>19<br />
</td>
<td>380<br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>20<br />
</td>
<td>400<br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>21<br />
</td>
<td>420<br />
</td>
<td><br />
</td>
<td>14/11<br />
</td>
</tr>
<tr>
<td>22<br />
</td>
<td>440<br />
</td>
<td><br />
</td>
<td>9/7<br />
</td>
</tr>
<tr>
<td>23<br />
</td>
<td>460<br />
</td>
<td>13/10<br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>24<br />
</td>
<td>480<br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>25<br />
</td>
<td>500<br />
</td>
<td>4/3<br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>26<br />
</td>
<td>520<br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>27<br />
</td>
<td>540<br />
</td>
<td><br />
</td>
<td>11/8, 15/11<br />
</td>
</tr>
<tr>
<td>28<br />
</td>
<td>560<br />
</td>
<td>18/13<br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>29<br />
</td>
<td>580<br />
</td>
<td><br />
</td>
<td>7/5<br />
</td>
</tr>
<tr>
<td>30<br />
</td>
<td>600<br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>31<br />
</td>
<td>620<br />
</td>
<td><br />
</td>
<td>10/7<br />
</td>
</tr>
<tr>
<td>32<br />
</td>
<td>640<br />
</td>
<td>13/8<br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>33<br />
</td>
<td>660<br />
</td>
<td><br />
</td>
<td>16/11, 22/15<br />
</td>
</tr>
<tr>
<td>34<br />
</td>
<td>680<br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>35<br />
</td>
<td>700<br />
</td>
<td>3/2<br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>36<br />
</td>
<td>720<br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>37<br />
</td>
<td>740<br />
</td>
<td>20/13<br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>38<br />
</td>
<td>760<br />
</td>
<td><br />
</td>
<td>14/9<br />
</td>
</tr>
<tr>
<td>39<br />
</td>
<td>780<br />
</td>
<td><br />
</td>
<td>11/7<br />
</td>
</tr>
<tr>
<td>40<br />
</td>
<td>800<br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>41<br />
</td>
<td>820<br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>42<br />
</td>
<td>840<br />
</td>
<td>13/8<br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>43<br />
</td>
<td>860<br />
</td>
<td><br />
</td>
<td>18/11<br />
</td>
</tr>
<tr>
<td>44<br />
</td>
<td>880<br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>45<br />
</td>
<td>900<br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>46<br />
</td>
<td>920<br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>47<br />
</td>
<td>940<br />
</td>
<td><br />
</td>
<td>12/7<br />
</td>
</tr>
<tr>
<td>48<br />
</td>
<td>960<br />
</td>
<td>26/15<br />
</td>
<td>7/4<br />
</td>
</tr>
<tr>
<td>49<br />
</td>
<td>980<br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>50<br />
</td>
<td>1000<br />
</td>
<td>16/9<br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>51<br />
</td>
<td>1020<br />
</td>
<td>9/5<br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>52<br />
</td>
<td>1040<br />
</td>
<td><br />
</td>
<td>11/6, 20/11<br />
</td>
</tr>
<tr>
<td>53<br />
</td>
<td>1060<br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>54<br />
</td>
<td>1080<br />
</td>
<td>15/8<br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>55<br />
</td>
<td>1100<br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>56<br />
</td>
<td>1120<br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>57<br />
</td>
<td>1140<br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>58<br />
</td>
<td>1160<br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>59<br />
</td>
<td>1180<br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td>60<br />
</td>
<td>1200<br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
</table>
<br />
<br />
<!-- ws:start:WikiTextHeadingRule:2:<h1> --><h1 id="toc1"><a name="Compositions"></a><!-- ws:end:WikiTextHeadingRule:2 -->Compositions</h1>
<a class="wiki_link_ext" href="http://eceserv0.ece.wisc.edu/%7Esethares/mp3s/rojqoq.html" rel="nofollow">Rojqoq (So-Called Peace)</a> <a class="wiki_link_ext" href="http://micro.soonlabel.com/gene_ward_smith/Others/Sethares/Rojqoq.mp3" rel="nofollow">play</a> by William Sethares<br />
<a class="wiki_link_ext" href="http://youtu.be/1rrgmP9VYQU" rel="nofollow">Skating On Thin Ice</a> <a class="wiki_link_ext" href="http://micro.soonlabel.com/gene_ward_smith/Others/Perry/Skating%20On%20Thin%20Ice.mp3" rel="nofollow">play</a><br />
<a class="wiki_link_ext" href="http://youtu.be/5GIZOYMkkJ0" rel="nofollow">My Mother Said So</a> <a class="wiki_link_ext" href="http://micro.soonlabel.com/gene_ward_smith/Others/Perry/My%20Mother%20Said%20So.mp3" rel="nofollow">play</a><br />
<a class="wiki_link_ext" href="http://www.macjams.com/song/62273" rel="nofollow">Black Salt - White Pepper</a> <a class="wiki_link_ext" href="http://micro.soonlabel.com/gene_ward_smith/Others/Perry/Black%20Salt%20-%20White%20Pepper.mp3" rel="nofollow">play</a><br />
<a class="wiki_link_ext" href="http://www.macjams.com/song/64413" rel="nofollow">NGC 300</a><a class="wiki_link_ext" href="http://micro.soonlabel.com/gene_ward_smith/Others/Perry/NGC%20300.mp3" rel="nofollow">play</a><br />
all by Robin Perry<br />
<a class="wiki_link_ext" href="http://x31eq.com/music/dingshi.mp3" rel="nofollow">Dingshi</a> and<br />
<a class="wiki_link_ext" href="http://x31eq.com/music/jitter.ogg" rel="nofollow">Gene's Jitterbug (ogg)</a> <a class="wiki_link_ext" href="http://micro.soonlabel.com/gene_ward_smith/Others/Breed/jitter.mp3" rel="nofollow">Gene's Jitterbug (mp3)</a> <a class="wiki_link_ext" href="http://x31eq.com/music/jitter60.pdf" rel="nofollow">Score</a><br />
by Graham Breed<br />
<br />
<!-- ws:start:WikiTextHeadingRule:4:<h1> --><h1 id="toc2"><a name="Images"></a><!-- ws:end:WikiTextHeadingRule:4 -->Images</h1>
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<!-- ws:start:WikiTextLocalImageRule:629:<img src="/file/view/blue_60edo.png/284591332/blue_60edo.png" alt="" title="" /> --><img src="/file/view/blue_60edo.png/284591332/blue_60edo.png" alt="blue_60edo.png" title="blue_60edo.png" /><!-- ws:end:WikiTextLocalImageRule:629 --><br />
<br />
<!-- ws:start:WikiTextLocalImageRule:630:<img src="/file/view/60edoguitar.jpg/312533826/60edoguitar.jpg" alt="" title="" /> --><img src="/file/view/60edoguitar.jpg/312533826/60edoguitar.jpg" alt="60edoguitar.jpg" title="60edoguitar.jpg" /><!-- ws:end:WikiTextLocalImageRule:630 --><br />
Robin Perry guitar</body></html>